Simplify the following expression: $ k = \dfrac{3x - 6}{-5x - 5} - \dfrac{-1}{6} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{3x - 6}{-5x - 5} \times \dfrac{6}{6} = \dfrac{18x - 36}{-30x - 30} $ Multiply the second expression by $\dfrac{-5x - 5}{-5x - 5}$ $ \dfrac{-1}{6} \times \dfrac{-5x - 5}{-5x - 5} = \dfrac{5x + 5}{-30x - 30} $ Therefore $ k = \dfrac{18x - 36}{-30x - 30} - \dfrac{5x + 5}{-30x - 30} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{18x - 36 - (5x + 5) }{-30x - 30} $ Distribute the negative sign: $k = \dfrac{18x - 36 - 5x - 5}{-30x - 30}$ $k = \dfrac{13x - 41}{-30x - 30}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{-13x + 41}{30x + 30}$